#on mind and matter

[rxshl]

ON INTUITION

In addition to empirical science and formal logic, there was now a third viable path to knowing truths: the path of metaphysics and intuition. By intuition, we mean insights experienced only within the mind; apprehensions of truths unreachable by empiricism or formal logic.

Through his incompleteness theorems—both their method and their content—Gödel affirmed an essential, irreducible role for intuitions in mathematics. He showed that there are some truths rigorously confirmed to be true, but which can be proved true only by some method other than formal logic, a method like direct intuitions. In doing so, he undid the logical positivist mission, resurrecting intuitions as a viable, scientifically credible path for how humans can know the true nature of things. Aspects of the universe that were not amenable to empiricism or logical proof might be amenable to experiences within the mind.

These ideas were not merely abstractions to Gödel. The American mathematician Rudy Rucker recounted how Gödel described the process of his mathematical intuition many years later: “One must close off the other senses, for instance by lying down in a quiet place,” Rucker wrote, paraphrasing Gödel. He continued, “The ultimate goal of such thought, and of all philosophy, is the perception of the Absolute.” Through this mild form of self-induced sensory deprivation, Gödel availed himself of an interior sense that, to him, was like any of the other senses of sight, smell, taste, hearing, and touch, except this one was a direct perception of mathematical objects and processes. “Despite their remoteness from sense experience,” Gödel wrote, “we do have something like a perception also of the objects of set theory [a form of mathematics], as is seen from the fact that the axioms force themselves upon us as being true. I don’t see any reason why we should have less confidence in this kind of perception, i.e., in mathematical intuition, than in sense perception, which induces us to build up physical theories and to expect that future sense perceptions will agree with them.

Such “remoteness from sense experience,” while still remaining “something like a perception” in the mind, is in fact an excellent definition of what the Vienna Circle meant by “metaphysics.” Gödel not only established truths of existence (in his case, mathematical truths) through mental contemplation alone; he simultaneously demonstrated that formal logic could not have done so itself. Metaphysical practice could solve problems that had resisted science and logic, despite long, significant efforts.

That there are statements that can be known to be true but cannot be logically proved as such indicates that there are mathematical truths that exist independently of logical, machinelike exercises in proof building. In other words, it is now a certainty that the universe cannot be entirely described, captured, and “proved” by such exercises in producing theorems from axioms. Formal logic is unable to be the final measure of all mathematical truths. Ultimately, some truths must always be apprehensible only by intuition.

Gödel’s accomplishment with the incompleteness theorems, then, was not simply to prove or disprove one particular arcane question about the Hilbert program. It was much more ambitious. By reasserting the importance of intuition in our scientific understanding of the structure and function of the universe, Gödel was able to restore mental intuition to respectability as a means of assessing truths, reopening science to at least consider insights from philosophy and, alas for the Vienna Circle, metaphysics. Such insights and speculations, if rigorously obtained, were now acceptable, even necessary modes of knowing truths.

[casserpillarr]

Spy what have you done..

[platypaws]

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pnf revival challenge day 18: Phineas!

Hosted by @howtonerdoutovereverything! ✨

I DIDNT MEAN TO LIE, I HAD NO PLANS OF CONTINUING THIS REVEAL THREAD AT ALL , DIRECTLY OR NOT, BUT THEN i dont know what happened and now i cant even say i wont continue it because i know for a fact ill try to get a some sorta ferb POV on the situation too hsdfugihgudsf

anyway this happens the same day as the reveal from day 9, just later at night, theyre all good, they talked it out by now but its still awkward i gUESS ����‍♂️

[chloesimaginationthings]

The nightmares in FNAF 4 get crazy...

[bellaciao-ciao-ciao]

[willosword]

Fake, facsimile, forgery.

[dawnatlas]

forever partner friday but it's on a saturday and i gave up halfway through so its messy as hell

anways... what's spookier than the nest am i right

[poorlydrawninstarsandtime]

really specific hangups

[ids in alt]

[lazylittledragon]

i am losing my entire shit right now, this single panel caused a nuclear disaster in my ig comments when someone said "halsin just saying 'astarion's partner' instead of his name feels icky"

which is such a fucking reach by itself but descended into this in about 5 seconds

[appeltjesgroen]

Happy (Draco finally had the guts to kiss Hermione) Valentine’s day~ 💕✨

[rxshl]

[cowardlykrow]

"NOW BREAK"

this was WAY funnier in my head...

[h20milk]

tfw you fall in love with the magicless prefect that keeps running around campus 🤦‍♀️

[fernsnailz]

misc recent transformers sketches

[bitterest-taste]

growing up is realising that spencer reid was always hot

maturing is realising that aaron hotchner was also fine as fuck the whole time

[biggest-gaudiest-patronuses]

probably will be FORCED by Pomp And Circumstance to go to the CLOWN HOSPITAL, for a CLOWN INJURY (may or may not be An ALLEGEDLY Fractured Foot...a MOURNFUL MALADY incurred in the most PATHETIC and LAPSIDAISICAL Fashion of TRAGICALLY UNFASHIONABLY Events......

Anyway. Forgot what I was saying. Buy me 1/25th of an x-ray or whatnot I guess